Catalyzes the first and rate-limiting reaction of the four reactions that constitute the long-chain fatty acids elongation cycle. This endoplasmic reticulum-bound enzymatic process allows the addition of 2 carbons to the chain of long- and very long-chain fatty acids (VLCFAs) per cycle. Condensing enzyme that catalyzes the synthesis of polyunsaturated very long chain fatty acid (C20- and C22-PUFA), acting specifically toward polyunsaturated acyl-CoA with the higher activity toward C20:4(n-6) acyl-CoA. May participate in the production of polyunsaturated VLCFAs of different chain lengths that are involved in multiple biological processes as precursors of membrane lipids and lipid mediators. {ECO:0000255|HAMAP-Rule:MF_03202, ECO:0000269|PubMed:11734209, ECO:0000269|PubMed:12371743, ECO:0000269|PubMed:19575253, ECO:0000269|PubMed:20937905}. This is the function of ELOVL2 (ELOVL fatty acid elongase 2, ENSG00000197977).